Superelastic graphene aerogel-based metamaterials

Ultralight, ultrastrong, and supertough graphene aerogel metamaterials combining with multi-functionalities are promising for future military and domestic applications. However, the unsatisfactory mechanical performances and lack of the multiscale structural regulation still impede the development of graphene aerogels. Herein, we demonstrate a laser-engraving strategy toward graphene meta-aerogels (GmAs) with unusual characters. As the prerequisite, the nanofiber-reinforced networks convert the graphene walls’ deformation from the microscopic buckling to the bulk deformation during the compression process, ensuring the highly elastic, robust, and stiff nature. Accordingly, laser-engraving enables arbitrary regulation on the macro-configurations of GmAs with rich geometries and appealing characteristics such as large stretchability of 5400% reversible elongation, ultralight specific weight as small as 0.1 mg cm−3, and ultrawide Poisson’s ratio range from −0.95 to 1.64. Additionally, incorporating specific components into the pre-designed meta-structures could further achieve diversified functionalities.

Contents 8 S1. Supplementary Notes 9 S1.1 Establishment of angle resolved radial distribution function. 10 S1.2 Molecular dynamics simulation.   116 LAMMPS is used to perform molecular dynamics simulations. 1 The coarse grain 117 model proposed by Cranford and et. is used in this work, 2 and the interaction parameters 118 are obtained in the same way, except the size of coarse grain is much larger. In our 119 simulation, graphene sheet is set to 4 um size square according to experiments, and the 120 coarse grain size is 0.25 um, which means one graphene sheet is composed by 17×17 121 coarse grain particles. The thickness of graphene sheet layer is set to 140 nm, and 122 average 2.5 layers at same place, which thus recovers 350 nm skeleton thickness 123 observed in experiments. Periodic boundary condition is used in our calculation model 124 (Please see Fig. 5a), and its box size is 30 um ×10 um ×20 um. With all this geometry, 125 the mass and interaction parameters for coarse grain particles could be obtained. To be 126 specific, mass equals 0.000475 pg, harmonic potential for bonds and angles are used, 127 and the spring coefficient for bonds k T equals 33607020 pg us −2 (the equilibrium 128 distance r0 = 0.25 μm), the spring coefficient for in-plane angles k phi equals 11725 pg 129 μm 2 ⋅μs −2 (the equilibrium angle φ0 = 90°), and the spring coefficient for out-plane 130 angles kθ equals 15737 pg μm 2 μs −2 ( the equilibrium angle θ0 = 180°). When 131 considering the effective thickness, if strain energy under tension is assumed to keep 132 unchanged only kθ changes N 2 times (N is the ratio between effective thickness and 133 original thickness), since it is the only parameter related to the bending modulus, and 134 The harmonic potential is used to describe bonds and angles between coarse grain 137 particles within one fiber. The bond spring coefficient k T,fiber = 78600 pg us −2 and 138 equilibrium distance 0, = 1 μm, and angle spring coefficient k T,fiber =49 pg us −2 139 um 2 and equilibrium angle 0, = 180 ∘ . Assuming single fiber mechanical 140 property shares same Young's modulus of graphene sheets, all these parameters could 141 be derived from experiments. To be specific, the around 200 nm typical diameter of 142 fibers, the graphene sheet surface occupying ratio, and the density difference induced 143 by including fibers are all taken into account. Note that one fiber represents multiple 144 fibers in reality, since only in this way the number of particles in our simulation could 145 be reduced to a computable range. The mass of fibers is estimated and taken 0.0088825 146 pg in our simulations. 147 Lenard Jones potential is used to depict Van der Waals interactions. Same surface 148 energy (260 mJ m −2 ) are used to both graphene sheets and fibers, 2 with different surface 149 area the coarse grain particles of graphene sheets and fibers have different epsilon, i.e. 150 epsilon = 32.5 pg μm 2 μs −2 and epsilon= 8 pg μm 2 μs −2 , respectively. Both equilibrium 151 distance related parameter sigma = 0.2 um. 152 The configuration of our calculation model is generated by ourselves and followed 153 by a minimization and then a molecule dynamics simulation with NVT ensemble to 154 relax the system, the obtained structure is shown in Fig. 5a. To simulate the 155 compression process, every time shrinking the box in Z dimension is followed by a 156 minimization. This is because the low density of this system, a direct molecule 157 dynamics run could have particles losing problem, which leads to breakdown of the 158

simulation. 159
Here, we normalized relationship of stress and strain to confirm the contribution 160 of toughening derived from bulk deformation process. As shown in Fig. 5b, we firstly 161 established a model of stress-strain curve (blue dotted curve), which describes an ideal 162 compression process only with buckling deformation. As displayed in Fig. 5c, bulk 163 deformation model is better for avoiding the extreme bending, which contributes to 164 maintain the complete structure of graphene walls during long-term compression 165 cycling, demonstrating a good fatigue-resistance property.

167
Finite element calculation 169 For finite element calculation, Abaqus is used to demonstrate the designability of 170 Poisson's ratio based on this material, where same sized structure and stress-strain curve 171 obtained in experiments are used. Note that experimental tensile and compression curve 172 of graphene foam is directly taken as a numerical constitutive relationship, which 173 corresponds to the low density foam constitutive model implemented in Abaqus. There 174 two things need to be clarified. First, the relaxation effect included in this model is set 175 to zero due to the slow loading rate in experiments. Second, this model assumes zero 176 Poisson's ratio, which is reasonable according to observations. 177 Specifically, with large compression over 50%, mechanical instability leads to 178 structure distortion, which is not observed in experiments. Thus, here only the variation 179 of Poisson's ratio before 50% compression is shown. And both 9-hole and 3-hole Here, in order to explore whether the fiber content would influence the mechanical 316 performances of the GmA, we prepared three samples with different fiber contents, 317 which rely on the feed weight ratio of PI fibers to GO. And the as-prepared GmAs were 318 nominated as 0.1-GmA (weight ratio of PI fibers to GO is 1:10), 0.3-GmA (weight ratio 319 of PI fibers to GO is 3:10), and 0.5-GmA (weight ratio of PI fibers to GO is 5:10), 320

respectively. 321
Note that typical thickness means frequently observed thicknesses but not a mean 322 value of thickness, since the graphene sheets are neither always nor strictly 323 perpendicular to the lens of the microscope. The free energy density is given by 335 that density of graphene skeleton 2 is taken as a density reference thus equals to one, 345 for example = 0.1 means the added fiber density is 0.1 times of 2 . As can be 346 seen in Supplementary Fig. 22, experimental stress-strain curves of graphene foam with 347 different density of nanofibers could be well described by our theoretical model (stress 348 equals to the derivative of ( ) with respect to compressive strain ). 349 Since the free energy density already include all relevant microscopic interaction 350 ways, that of a typical microstructure i.e. local graphene skeleton, should have the same 351 form but different parameters. Taking advantage of this form, Young's modulus is 352 found to be proportional to the initial value of fiber density ;0 ( at the undeformed 353 state), which contribute to the enhancement of bending stiffness = 3 /12(1 − 2 ), 354 where t is the thickness of graphene skeleton and is Poisson's ratio. Compared with common materials, negative Poisson's ratio materials have 379 superior shear resistance, indentation resistance, and fracture toughness, which makes 380 them suitable for energy absorption applications, such as aerospace, defense, and sports 381 protection. for the GmA with low density, although it can no longer guarantee its 382 application in mechanical energy absorption, light skeletons will be more sensitive to 383 stress and strain. Supplementary Fig. 26 shows under the condition of small strain, the 384 GmA with negative Poisson's ratio, such as GmA−0.7 and GmA−1.2, exhibits larger gauge 385 factor (GF) compared with the GmA without any holes, demonstrating the better 386 sensitivity. The GF is calculated by (ΔR/R0)/ε, where ΔR is the resistance change under 387 compression and R0 is the resistance before straining. Additionally, the ultra-light GmA 388 can be used as a platform to incorporate other particles to achieve more functionalities.

389
The magnetically responsive actuator was demonstrated by the low density GmA in 390 Supplementary Fig. 27. are stable in air when the temperature is below 500 °C (Supplementary Fig. 28b). In a 412 nitrogen atmosphere, the GmA are stable when the temperature is below 550 °C 413 ( Supplementary Fig. 28c). However, the TGA curve of GmA in air presents three 414 distinct regions (Supplementary Fig. 28d). (1) In the process of increasing the 415 temperature from 50 to 500 °C, the GmA has almost no weight loss (less than 1%), 416 indicating that the reduced graphene oxide and PI nanofibers are stable below 500 °C. 417 (2) As the temperature is higher than 500 °C, the weight loss of GmA begins again, 418 which is derived from the oxidation reaction of reduced graphene oxide and 419 decomposition of the polymer carbon backbone. (3) As the temperature is higher 600 °C, 420 the weight of residual carbon skeletons is constant. 421 The viscoelastic properties of the GmAs are characterized by the dynamical 422 mechanical analysis (DMA). The nearly constant storage modulus, loss modulus, and 423 damping ratio within a wide temperature range from −100 to 300 °C (Supplementary 424 Fig. 28e) demonstrates that the elastic behavior of GmA is invariant with the 425 temperature, which is an enthalpic elasticity rather than the entropic elasticity.  Fig. 30). But to be 443 noted, the strength of ceramic aerogels still needs to be improved ( Supplementary Fig.  444 30f), which is excluded in this work because it is a systematic work involving the 445 optimization of the complex calcination and crystallization process.

478
In general, laser processing involves rapid energy input and energy deposition on 479 a solid's surface. The pulsed/continuous laser energy is absorbed by the electrons in this 480 process. Then the electrons interact with the lattice to complete the energy transfer 481 (10 −11 −10 −12 s). And the thermal equilibrium is established between the lattices with 482 increasing temperature and kinetic energy of the lattice. The resultant temperature 483 depends on the absorbed energy, thermal diffusion rate of materials, and work 484 conditions during laser irradiation. In our experiment, the average temperature of the 485 laser spot is about 1000 °C, and the instantaneous temperature of laser is as high as 486 1300 °C, which is measure by a thermocouple with a metal probe. At this temperature, 487 the graphene and PI will be rapidly oxidized by oxygen. The thermogravimetric 488 analysis/mass spectrometry (TGA-MS) measurement confirmed that once the 489 temperature exceeds 500 °C, the PI and GmA would generate a lots of combustion 490 products, such as CO2 (m/z:44), CO (m/z:28), H2O (m/z:18), and a small amount of 491 nitride ( Supplementary Fig. 35a, b). During this process, the GmA is sculpted with hole 492 structures ( Supplementary Fig. 35c). However, the fast energy input of laser often 493 makes the spot enlargement and have a wider engraving area. The smallest laser-494 engraving size that this nanosecond laser machine can achieve is 200 μm. And, the 495 precise processing resolution is about 1 mm. At the surface of graphene layers, the gases generated from the rapid combustion 502 of graphene and PI will produce fast-flowing airflow that can break the graphene walls 503 and result in partially cracked structures (Marked in red circles in Supplementary Fig.  504 R36a). In contrast, the GmA surface ripped by hands exhibits a relatively complete 505 structure without obvious fractures ( Supplementary Fig. 36b). Additionally, because the 506 temperature at the edge of the laser may be lower than that at the spot center. Some 507 insufficient combusted flocs are often left on the laser-engraving surface 508 ( Supplementary Fig. 36c, e). In contrast, the tearing sufaces of graphene walls show a 509 smooth structure ( Supplementary Fig. 36d, f).